The proposed research will develop methods for the analysis of serial measurements obtained in longitudinal studies. Such studies involve the repeated observation of individuals (or experimental units), at different time points and possibly under differing experimental conditions. These studies are increasingly common in medicine and public health; they include clinical and laboratory studies as well as epidemiological investigations. The objectives of longitudinal studies normally include the analysis of trends, rates of change, or growth. No unified approach currently exists for handling these common problems. Most statistical methods in widespread use are inappropriate because they assume independent observations; methods for dependent observations are complicated to implement and to interpret. We propose to develop a unified approach to the analysis of serial measurements, including growth curves and repeated measures data, based on the use of two-stage random effects models. These models have natural appeal to investigators, since they model explicity both population and individual characteristics. We will use maximum likelihood as the basis for estimation and inference, and the E-M algorithm for computation. Recent advances in theory and methods related to these two topics make this an opportune time to undertake this research. The research will proceed in parallel for measured and categorical response. For measured data we will particularize the general linear mixed model theory to longitudinal data and develop the appropriate software for implementation. For categorical response data we will investigate the feasibility of implementing an analogous class of models. We will assess the desirability and practicality of the widespread use of two-stage random effects models in the context of our own applied research. In summary, our broad objectives are to develop, implement and disseminate to practicing statisticians a unified methodology for the analysis of serial measurements.